learning objectives in this chapter you will learn about the t-test and its distribution t-test for...
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Learning Objectives
In this chapter you will learnabout the t-test and its distributiont-test for related samplest-test for independent samples
hypothesis testinghow to use SPSS to test for differences between means
t Distribution
In Chapter 6, you were introduced to the Normal Distribution
In this chapter, we will explore another distribution– t distribution
t Distribution
If the sample size is less than 30–use the t distribution
•to calculate confidence intervals–as sample size increases
•t distribution approximates the normal distribution
•the shape of t distribution is not fixed
Hypothesis Testing
Hypothesis testing•based on sample evidence
and probability theory•used to determine whether
the hypothesis should or should not be rejected
Important Terms
Null Hypothesis• A statement about the expected
value of a population parameterAlternative Hypothesis• Research statement that is
accepted– if the sample data suggest that the
null hypothesis should be rejected
Type I & Type II Errors
Type I Error•Rejecting the null hypothesis
when it is actually trueType II Error ()
•Accepting the null hypothesis when it is actually false
Type I Errors
The chance of making a Type I error is known as the level of significance or the alpha level ()– it is set by the researcher– the convention is to use the .05
level of significance as the probability of committing Type I error
Steps in Hypothesis Testing
One-tailed or two-tailed test?
Do not reject null Reject null and accept alternative
Step 5: Reach a decision
Step 4: Collect and analyze data
Step 3: Identify appropriate statistic
Step 2: Select a level of significance
Step 1: State null and alternative hypotheses
The Null Hypothesis
The research hypothesis is not tested directly– Instead, we test the null hypothesis
(H0): the hypothesis of no difference or no relationship
– We can never prove a hypothesis to be true
– Instead, we are searching for instance when it is not true
Accept or Reject?
Compare the test statistic (obtained value) to the alpha level and decide if it is greater or less than alpha– if less than, reject H0
– if greater than, retain H0
Decisions Under the Null Hypothesis
t Test
We frequently want to compare means–different tests based on sample•paired t test for related sample•independent t test when samples
are not related somehow
SPSS Procedure
The following slides demonstrate the independent t test–don’t forget to
•test for equality of variance•define the group either by specifying a
group number (discrete variable) or by using the cut point (perhaps the median) if the variable is continuous
SPSS Step 1
Open data set
SPSS Step 2
Select Compare Means and then Independent Samples T Test
SPSS Step 3
Select the test variable and then the grouping variable
SPSS Step 4
Define the groups or use the Cut Point to divide a continuous-level variable
SPSS Step 5
Mouse Click OK to obtain results
SPSS Output